[EM] hybrid 2-stage and 1-stage Bayesian Regret for comparing multiwinner election systems

[Kristofer Munsterhjelm]

Warren Smith wrote:
>> All your other knobs are input knobs, no? The #candidates, #winners,
>> utility generation models and parameters, etc., specify what kind of
>> data is run through the voting methods (and subsequent utility
>> determination function), whereas the weight-knob is an adjustment of the
>> (combined) utility function itself.
>>
>> So it would seem to be a quite different sort of knob. Adjusting it
>> would be similar to adjusting 1-stage BR between, say, mean utility and
>> worst utility (maximin).
> 
> --I don't agree that it is a "different" kind of knob.  It's just another knob.
> Your claim the others are "input" knobs is an arbitrary judgment by you, and
> I can regard at least some of them as "not input" equally validly/arbitrarily.

Are you claiming that the separation into input/not-input (as opposed to 
some other divide) is arbitrary, or that my labeling of the weighting as 
output rather than input is arbitrary?

If it is the latter, I would disagree. Input is that which, when 
changed, changes what is supplied to the voting methods under test. 
Output is that which could be adjusted even if the voting methods were 
run only once: i.e. parameters regarding how to interpret the results 
from the voting methods themselves, with respect to the utility data 
already supplied.

Or in other words: if you give me only the utility data and the output 
from the voting methods, for each round, I can calculate the results for 
many different output knob settings, but not input knob settings.

> I also don't agree that maximin utility should be of interest.

The comparison did not, as a comparison, regard whether maximin should 
be of interest or not, but rather attempted to show the category 
division in another manner. If I have the round results (and utility 
data) for each round, I can find both mean and maximin utility (and 
median, interquartile, you name it), but I can't simulate the results 
for another number of candidates (unless I clone some of the candidates, 
for instance).

In the more indirect sense, you might claim that if you don't agree that 
maximin utility should be of interest, there's no need to introduce it 
as a knob in the first place. What the comparison said, though, was that 
if others disagreed, then the question of what weight to choose (between 
mean and maximin, or just all-one and none of the other) would be 
similar to the question of what weight to choose between 1-stage and 
2-stage BR, and the same arguments for (e.g.) doing a 2D diagram rather 
than just a weighted combination, would apply.